We build two embedded resolution procedures of a quasi-ordinary singularity of complex
analytic hypersurface, by using toric morphisms which depend only on the characteristic
monomials associated to a quasi-ordinary projection of the singularity. This result
answers an open problem of Lipman in Equisingularity and simultaneous resolution of
singularities, Resolution of Singularities, Progress in Mathematics No. 181, 2000, 485-
503. In the first procedure the singularity is embedded as hypersurface. In the second
procedure, which is inspired by a work of Goldin and Teissier for plane curves (see
Resolving singularities of plane analytic branches with one toric morphism, loc. cit.,
pages 315-340), we re-embed the singularity in an affine space of bigger dimension in
such a way that one toric morphism provides its embedded resolution. We compare both
procedures and we show that they coincide under suitable hypothesis.